Affine Lie Algebras And Quantum Groups

Author : Jürgen Fuchs
Publisher : Cambridge University Press
ISBN 13 : 9780521484121
Total Pages : 452 pages
Book Rating : 4.2X/5 ( download)

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Download or read book Affine Lie Algebras and Quantum Groups written by Jürgen Fuchs and published by Cambridge University Press. This book was released on 1995-03-09 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

Author : Jürgen A. Fuchs
Publisher : Cambridge University Press
ISBN 13 : 9780521415934
Total Pages : 447 pages
Book Rating : 4.34/5 ( download)

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Download or read book Affine Lie Algebras and Quantum Groups written by Jürgen A. Fuchs and published by Cambridge University Press. This book was released on 1992-10-08 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to the theory of affine Lie algebras and to the theory of quantum groups. It is unique in discussing these two subjects in a unified manner, which is made possible by discussing their respective applications in conformal field theory. The description of affine algebras covers the classification problem, the connection with loop algebras, and representation theory including modular properties. The necessary background from the theory of semisimple Lie algebras is also provided. The discussion of quantum groups concentrates on deformed enveloping algebras and their representation theory, but other aspects such as R-matrices and matrix quantum groups are also dealt with.

Author : Naihuan Jing
Publisher : American Mathematical Soc.
ISBN 13 : 0821811991
Total Pages : 482 pages
Book Rating : 4.93/5 ( download)

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Download or read book Recent Developments in Quantum Affine Algebras and Related Topics written by Naihuan Jing and published by American Mathematical Soc.. This book was released on 1999 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying "centre stage" in the theory of infinite dimensional Lie theory.

Author : Andrew Pressley
Publisher : Cambridge University Press
ISBN 13 : 9781139437028
Total Pages : 246 pages
Book Rating : 4.2X/5 ( download)

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Download or read book Quantum Groups and Lie Theory written by Andrew Pressley and published by Cambridge University Press. This book was released on 2002-01-17 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises an overview of the material presented at the 1999 Durham Symposium on Quantum Groups and includes contributions from many of the world's leading figures in this area. It will be of interest to researchers and will also be useful as a reference text for graduate courses.

Author : Vyjayanthi Chari
Publisher : Cambridge University Press
ISBN 13 : 9780521558846
Total Pages : 672 pages
Book Rating : 4.40/5 ( download)

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Download or read book A Guide to Quantum Groups written by Vyjayanthi Chari and published by Cambridge University Press. This book was released on 1995-07-27 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory, and has thrown new light on many different topics, notably low-dimensional topology and conformal field theory. The goal of this book is to give a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Thus this book can serve both as an introduction for the newcomer, and as a guide for the more experienced reader. All who have an interest in the subject will welcome this unique treatment of quantum groups.

Author : N.Ja. Vilenkin
Publisher : Springer Science & Business Media
ISBN 13 : 940172881X
Total Pages : 651 pages
Book Rating : 4.12/5 ( download)

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Download or read book Representation of Lie Groups and Special Functions written by N.Ja. Vilenkin and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the last of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with q-analogs of special functions, quantum groups and algebras (including Hopf algebras), and (representations of) semi-simple Lie groups. Also treated are special functions of a matrix argument, representations in the Gel'fand-Tsetlin basis, and, finally, modular forms, theta-functions and affine Lie algebras. The volume builds upon results of the previous two volumes, and presents many new results. Subscribers to the complete set of three volumes will be entitled to a discount of 15%.

Author : Toshiaki Shoji
Publisher : American Mathematical Society(RI)
ISBN 13 :
Total Pages : 514 pages
Book Rating : 4.39/5 ( download)

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Download or read book Representation Theory of Algebraic Groups and Quantum Groups written by Toshiaki Shoji and published by American Mathematical Society(RI). This book was released on 2004 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. This title presents an overview of developments in representation theory of algebraic groups and quantum groups. It includes papers containing results concerning Lusztig's conjecture on cells in affine Weyl groups.

Author : Bangming Deng
Publisher : American Mathematical Soc.
ISBN 13 : 0821841866
Total Pages : 790 pages
Book Rating : 4.60/5 ( download)

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Download or read book Finite Dimensional Algebras and Quantum Groups written by Bangming Deng and published by American Mathematical Soc.. This book was released on 2008 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more strikingly apparent. This text combines, for the first time in book form, the theories of finite dimensional algebras and quantum groups. More precisely, it investigates the Ringel-Hall algebra realization for the positive part of a quantum enveloping algebra associated with a symmetrizable Cartan matrix and it looks closely at the Beilinson-Lusztig-MacPherson realization for the entire quantum $\mathfrak{gl}_n$. The book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the representation theory of quivers with automorphisms and the theory of quantum enveloping algebras associated with Kac-Moody Lie algebras. These two independent theories eventually meet in Part 4, under the umbrella of Ringel-Hall algebras. Cartan matrices can also be used to define an important class of groups--Coxeter groups--and their associated Hecke algebras. Hecke algebras associated with symmetric groups give rise to an interesting class of quasi-hereditary algebras, the quantum Schur algebras. The structure of these finite dimensional algebras is used in Part 5 to build the entire quantum $\mathfrak{gl}_n$ through a completion process of a limit algebra (the Beilinson-Lusztig-MacPherson algebra). The book is suitable for advanced graduate students. Each chapter concludes with a series of exercises, ranging from the routine to sketches of proofs of recent results from the current literature."--Publisher's website.

Author : Leonid I. Korogodski
Publisher : American Mathematical Soc.
ISBN 13 : 0821803360
Total Pages : 162 pages
Book Rating : 4.63/5 ( download)

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Download or read book Algebras of Functions on Quantum Groups: Part I written by Leonid I. Korogodski and published by American Mathematical Soc.. This book was released on 1998 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text is devoted to the study of algebras of functions on quantum groups. The book includes the theory of Poisson-Lie algebras (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions and the theory of quantum Weyl groups. It can serve as a text for an introduction to the theory of quantum groups and is intended for graduate students and research mathematicians working in algebra, representation theory and mathematical physics.

Author : Jacob Greenstein
Publisher : Birkhäuser
ISBN 13 : 9783030638511
Total Pages : 0 pages
Book Rating : 4.10/5 ( download)

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Download or read book Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification written by Jacob Greenstein and published by Birkhäuser. This book was released on 2023-03-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.